Design and Analysis of Linear Quadratic Regulator for a Non-Linear Positioning System

Abstract:

The control of rotary inverted pendulum is a case of classical robust controller design of non-linear system applications. In the control system design, a precise system model is a pre-requisite for an enhanced and optimum control performance. This paper describes the dynamic system model of an inverted pendulum system. The mathematical model was derived, linearized at the upright equilibrium points and validated using non-linear least square frequency domain identification approach based on measured frequency response function of the physical system. Besides that, a linear quadratic regulator (LQR) controller was designed as the balancing controller for the pendulum. An extensive analysis was performed on the effect of the weighting parameter Q on the static time of arm, balance time of pendulum, oscillation, as well as, response of arm and pendulum, in order to determine the optimum state-feedback control vector, K. Furthermore, the optimum control vector was successfully applied and validated on the physical system to stabilize the pendulum in its upright position. In the experimental validation, the LQR controller was able to keep the pendulum in its upright position even in the presence of external disturbance forces.

• Periodical: Applied Mechanics and Materials (Volume 761)
• Pages: 227-232
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.761.227
• Online since: May 2015
• Authors: Tang Teng Fong, Zamberi Jamaludin*, Ahmad Yusairi Bani Hashim, Muhamad Arfauz A. Rahman
• Keywords: Frequency Domain Identification, Linear Quadratic Regulator, Mathematical Modelling, Non-Linear System, Rotary Inverted Pendulum, System Identification

References

[1] K. Barya, S. Tiwari, R. Jha, Comparison of LQR and Robust Controllers for Stabilizing Inverted Pendulum System, IEEE International Conference on Communication Control and Computing Technologies, pp.300-334, Oct (2010).

DOI: 10.1109/icccct.2010.5670570

[2] M. Akhtaruzzaman, A.A. Shafie, Modeling and Control of a Rotary Inverted Pendulum using Various Methods, Comparative Assessment and Result Analysis, IEEE International Conference on Mechatronics and Automation, pp.1342-1347, Aug (2010).

DOI: 10.1109/icma.2010.5589450

[3] S. Jadlovska, J. Sarnovsky, Application of the State-Dependent Riccati Equation Method in Nonlinear Control Design for Inverted Pendulum Systems, IEEE 11th International Symposium on Intelligent Systems and Informatics, pp.209-214, Sept (2013).

DOI: 10.1109/sisy.2013.6662572

[4] P. Ernest, P. Horacek, Algorithms for Control of a Rotating Pendulum, 19th IEEE Mediterranean Conference on Control and Automation, Jun (2011).

[5] P. Xue, W. Wei, An Analysis on the Kinetic Model of a Rotary Inverted Pendulum, and Its Intelligent Control, International Conference on Computational and Information Sciences, pp.978-981, Dec (2010).

DOI: 10.1109/iccis.2010.241

[6] A.A. Shojaei, M.F. Othman, R. Rahmani, M.R. Rani, A Hybrid Control Scheme for a Rotational Inverted Pendulum, UKSim 5th European Symposium on Computer Modeling and Simulation, pp.83-87, Nov (2011).

DOI: 10.1109/ems.2011.79

[7] T.T. Fong, Z. Jamaludin, L. Abdullah, System identification and modelling of rotary inverted pendulum, Int. J. Adv. Eng. Technol. 6(6) (2014) 2342-2353.

[8] K. Halder, N. Patra, Impact of Weighting Matrices in the Design of Discrete Optimal Controller based on LQR Technique for Non-Linear System, International Conference on Computer Communication and Informatics, pp.1-6, Jan (2013).

DOI: 10.1109/iccci.2013.6466157

[9] O. Oral, L. Cetin, E. Uyar, A novel method on selection of Q and R matrices in the theory of optimal control, Int. J. Syst. Control 1(2) (2010) 84-92.